I just spend a day troubleshooting Software updates errors at a customer site and thought I would share my experiences. 
The error codes are all found in the report Last scan state by collection

Error code on client Solution
16398 If you search the web you will get many hits on this error. The solution is to apply this WSUS 3.0 SP1 patch http://www.microsoft.com/downloads/details.aspx?FamilyId=6AA8A49D-170C-4077-8B9B-61F7BF5A1281&displaylang=en

Once the update is applied you can force a scan on the client. Monitor the ScanAgent.log file
1682 This is a classic error. Check the wuahandler.log file and it will report that the local wsus settings (applied by the Configuration Manager) is overwritten by a higher authority. That higher authority is most likely a group policy.

If you are certain that all WSUS group policies has been removed then verify that the client is actually applying group policies. I had 40-50 machines that for some reason didn’t apply their group policies. Those were joined to a workgroup and rejoined to the domain.

1683 Reinstall the Windows Update Agent causes error 0X800703E3

 

If you are still out of luck try running this from a bat file:

cd %windir%\system32
regsvr32 wuapi.dll /s
regsvr32 wuaueng.dll /s
regsvr32 wuaueng1.dll /s
regsvr32 wucltui.dll /s
regsvr32 wups.dll /s
regsvr32 wups2.dll /s
regsvr32 wuweb.dll /s
net stop wuauserv
net stop bits
rmdir /S /Q %windir%\softwaredistribution
net start wuauserv
net start bits
exit /B 0